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In this paper, the online learning capability and the robust property for the learning algorithms of cerebellar model articulation controllers (CMAC) are discussed. Both the traditional CMAC and fuzzy CMAC are considered. In the study, we find a way of embedding the idea of M-estimators into the CMAC learning algorithms to provide the robust property against outliers existing in training data. An annealing schedule is also adopted for the learning constant to fulfil robust learning. In the study, we also extend our previous work of adopting the credit assignment idea into CMAC learning to provide fast learning for fuzzy CMAC. From demonstrated examples, it is clearly evident that the proposed algorithm indeed has faster and more robust learning. In our study, we then employ the proposed CMAC for an online learning control scheme used in the literature. In the implementation, we also propose to use a tuning parameter instead of a fixed constant to achieve both online learning and fine-tuning effects. The simulation results indeed show the effectiveness of the proposed approaches.